Q:

Rob is making a tent out of canvas in the shape of a square pyramid. Each side of the square base is 6 feet long, and the height is 6.3 feet. If rob filled the tent with balloons, which measurement BEST describes the amount of balloons in the tent? (round to nearest whole number) A) 76 ft2 B) 120 ft2 C) 76 ft3 D) 120 ft3

Accepted Solution

A:
The amount of balloons in the tent is 125.075 feet cube. From the given options, approximately, option D is correct Solution:Given, Rob is making a tent out of canvas in the shape of a square pyramid.  Each side of the square base is 6 feet long, and the height is 6.3 feet.  Rob filled the tent with balloons,  We have to find which measurement BEST describes the amount of balloons in the tent?  As tent if filled with balloons the amount of balloons equals with volume of tent. Volume of tent is given as:[tex]\text { volume of tent }=a^{2}+2 a \sqrt{\frac{a^{2}}{4}+h^{2}}[/tex] where "a" is side length and "h" is height.[tex]\begin{array}{l}{\text { Then, Volume }=6.3^{2}+2(6.3) \sqrt{\frac{6.3^{2}}{4}+6^{2}}} \\\\ {=39.69+12.6 \sqrt{9.925+36}} \\\\ {=39.69+12.6 \times 6.7766=39.69+85.385} \\\\ {=125.075 \mathrm{ft}^{3}}\end{array}[/tex]Hence, from the given options, approximately, option D is correct.